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You may have lost the standby power supply. There should be a 5v supply
that runs with the set in standby, see if you can find that. Also check
for B+ (around 160VDC) at the large filter capacitors in the power
supply.

Compaq MV 540 (old dog monitors) DEAD 100% DEAD.
OSD dead too. it seems.
built in year 2000, its 17 years old, and you fix things that old
why> why do that, used LCD can be had for 20 bucks.
why slave over any relic CRT like this,,, for a musiem??
using the VGA cable
the monitor will go to sleep, lacking any PC sync lines Vert/horz
by design per VESA rules on that !
step one , use a PC.
set the PC up to do the max resolution on the CRT
some PC cant do that, (new PC)
im reading your users guide now, 1sec, google , hit.
first force the PC to 1024x768 resolution and 60 vert. refresh max.
now the CRT can work an not any of above number higher .
see? use working monitor to do that FIRST.

now plug in the vga,cable last. on the monitor under test.

power led means
green = power ok
amber or yellow are sleep or standby.
so that means, there is no sync.
or if the OSD works (does it>) turn the silly sleep timer off in the monitor. via OSD .

the operators guide, tells you to go to PC safe mode.
this mode sets reso real low. 800x600 and all monitors work there.
no sleep timer inside monitor i can find.,

lots of ways for any CRT to fail even the CRT itself
(loss of sweep)
loss of cathode video drive
the VGA card inside, can fail. killing dead all cathod drive.
the power supplies or regs inside can fail.
the HV can fail. 10,000 volts (dont touch it if long life is good)
some survive, or fly back hit head on wall and crush skull,
seen it and done it so,,, there you go.(ripped gash in arm once)
the 2nd anode is very high voltage, avoid it, and win,.
respect it.

sounds like you have a dead switching suppy. On these sets the best way to trouble shoot the power suppy is disconnect the horizontsl output and measure it Is it shorted yes replace the fly and the transistor and resolder several cold joints in the horizontal drive curcuit as well as in the main switching supply. If the HOT not shorted then your gonna need a service manual unless you shotgun the repair. Good Luck